This article proposes that paradigmatic conversations involve the development of a collective cognitive profile of the parties. This occurs through the negotiation of a series of collective beliefs. Collective beliefs are constituted by commitments that are joint in a sense that is explained. The parties to any joint commitment have associated rights and obligations. This helps to entrench a given collective belief once established. Even when interlocutors do not manage to negotiate a collective belief whose content has explicitly been specified, they are likely to establish one or more associated implicit collective beliefs. This supports the idea of a conversation as a collective activity whose stages are marked by the development of a relatively stable collective cognitive profile of the parties. This idea is briefly related to some of the existing literature on conversation, including classic articles by Stalnaker and Lewis on presupposition and conversational score.